Christos Athanasiadis: Equivariant gamma-positivity
Tid: On 2018-08-29 kl 10.15 - 11.15
Plats: Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH
Medverkande: Christos Athanasiadis, University of Athens
Abstract
Gamma-positivity is a powerful method to prove unimodality for polynomials with real symmetric coefficients. It appeared in the seventies, in work of Foata and Sch\"utzenberger on the Eulerian polynomials and attracted attention more recently, after work of Br\"anden on poset Eulerian polynomials and Gal on flag triangulations of spheres. This talk will focus on a natural equivariant analogue of this concept. Basic examples generalize the gamma-positivity of Eulerian, derangement and binomial Eulerian polynomials and their analogues for r-colored permutations. Open questions, and some theorems, coming from group actions on simplicial complexes, toric varieties and Rees products of posets, will be discussed.